Sequential nuclear explosion fracturing of geological formations

ABSTRACT

A vertically spaced series of nuclear explosive devices are emplaced in a subterranean formation and the lowermost explosive is detonated first to provide a nuclear chimney having an apical void spaced therein. The next higher device is then detonated to cause a generally cylindrical plug region to be displaced downwardly partially into said void space while creating a nuclear chimney similar to the first and the procedure is repeated with successively higher of the emplaced devices. A fractured shear of fault zone surrounds the cylindrical plug while an extensive pattern of radial fractures are created thereabout as well as about the shot cavity and associated chimney. More economical and effective results can be obtained as required, e.g., in stimulating production from petroliferous formations.

Elite States Patent Terhune Jan. 23, 1973 Primary ExaminerStephen J. Novosad AttorneyRoland A. Anderson [57] ABSTRACT A vertically spaced series of nuclear explosive devices are emplaced in a subterranean formation and the lowermost explosive is detonated first to provide a nuclear chimney having an apical void spaced therein. The next higher device is then detonated to cause a generally cylindrical plug region to be displaced downwardly partially into said void space while creating a nuclear chimney similar to the first and the procedure is repeated with successively higher of the emplaced devices. A fractured shear of fault zone surrounds the cylindrical plug while an extensive pattern of radial fractures are created thereabout as well as about the shot cavity and associated chimney. More economical and effective results can be obtained as required, e.g., in stimulating production from petroliferous formations.

3 Claims, 25 Drawing Figures PATENTEDJAH 23 1975 SHEET 1 [1F 9 SPECIFIC VOLUME-cc/g 19.4

Cavity Radius (Re) .w M m ddwlu. W D Udall .l e w H OMYIA. e H s 2 r BMW 4 C l 0 2 l6 0, W 4| H00" Wu %5c .0 W l 0X0 1W1 U LLILLLLM 8 0 2 4 2 2 1 3 A l 0 m v c 4 EL CM mm. CO V 6 8 0 0.30 0.42 SPECIFIC VOL UM E- cc/g.

8. wumamwumm INVENTOR.

Rob err W. Terhune ATTORNEY.

PAIfNTEnJAnzslsu 3.712.374

sum 2 or 9 INVENTOR. Robert Wv Terhun e E2 BY ATTORNEY.

Radial Distance -m VELOCITY- m/sec PATENTEDJAN 23 I975 SHEET t [1F 9 Fracture initiation 40- 3 Shock x from I Radial fractures I i N 30- Limit of compressive ",1,

failure 5 3 "m 20- Shear and radial fractures O l l TIME- msec WAGON WHEEL m LU 0 m 10 2 z x Q a: 10 c.)

--Hoggar granite 32- Wagon WheeHsol'id) Cracked ww --NTSgranite(dry,solid) 24- Picture Cliff sandstone ---NTS granite and Lewis 16 shale(wet,fractured) |'==(a,+ a )lZ-kbar Fig. 7

80 l G) Cavity radius Re Crushed radius Rb (3D Shear fracture Rf DISTANCE-m Fig.9

INVENTOR. Robert W Terhune BY WWW ATTORNEY.

Crack Number PATENTEDJAH23 I975 3.712.374

SHEET 7 [If 9 Limit of: @Cavity radius @Crush radius @Shear fracture radius @Radial fracture radius 0 10o kt (calc. No.5)

in (cute. No.4)

l l l l l l l l 0 20 40 I60 Horizontal Distance-m 1o- Fig.1?

2 Range-r/w (m/kt 2 10 I I Shear fracture limit a, {at 10,000 ft. D08 .3 t 1 1 1 Radial fracture 10 L mess (limit at 10,000 0 (P -P ft. DOB 3 3 o o i 10 --Radial 10 E 9 stress i ove .2 o u -1 x 2 1O 10 1 10 10 10 F1920 INVENTOR. Robert W Terhune 1o ta 10 4 M 4- W 10 Ranger/w m/ttt ATTORNEY.

PATENTEDJAN 23 ms sum 8 UF 9 Radius 1 Depth in thousand ft. I

overburden pressure bars Radial froctu re Crushed zone Depth in thousand fi. 2 4 6 8 lllll overburden pvessu re bars IN VEN TOR.

Robert W Terhune ATTORNEY.

SEQUENTIAL NUCLEAR EXPLOSION FRACTURING OF GEOLOGICAL FORMATIONS BACKGROUND OF THE INVENTION This invention was made under or in the course of USAEC Contract No. W-7405- ENG-48 with Unites States Atomic Energy Commission.

A number of proposals have been made heretofore relating to the use of nuclear explosives for fracturing or otherwise modifying petroliferous and other subterranean formations, for example, to stimulate production of natural gas and other hydrocarbons therefrom. Use of single or horizontally spaced detonation locations, applicable to relatively thin, i.e., less than about 500 feet thick formations, have usually been those considered. See, for example, U.S. Pat. No. 3,409,082, issued to Bray et al., Nov. 5, i968 and Proceedings of Symposium on Engineering With Nuclear Explosives CONF-700101 (Vol. 1) issued May 1970 and available from the clearinghouse for Federal Scientific and Technical Information, National Bureau of Standards, U.S. Department of Commerce, Springfield Va. 22151. However, U.S. Pat. No. 3,303,881, issued Feb. 14, 1967 to R. P. Dixon discloses a procedure in which a second nuclear explosive is detonated to cage oil shale into a cavity created by a first detonation for in situ production of hydrocarbons. Two, single nuclear detonation experiments, Gasbuggy and Rulison, have been conducted heretofore as described, e.g., at pp. 662- 697 and 597-620, of said Proceedings.

As contrasted to relatively thin petroliferous formations, including natural gas deposits, there exists very large reservoir formations having relatively thick continuous strata or complexes of gas bearing strata interbedded with barren impervious layers in which large reserves of natural gas are present but which have a permeability too low to permit economic production.

For example, the Uinta, Piceance, Green River and San Juan basins in Wyoming, Utah, Colorado and New Mexico have characteristics and reserves which are believed potentially recoverable using nuclear explosives as set forth in the following table.

seismic effects usually impose a severe restriction on the total nuclear detonation yield of single or simultaneously fired nuclear explosives so that one cannot usually resort merely to use of larger explosive yields to obtain vertical fracturing. Moreover, with larger yields the possibility of venting to the surface is increased. As disclosed by Nordyke, a plurality of nuclear explosives are emplaced in vertically spaced locations, preferably simultaneously in a single borehole and are detonated sequentially upwardly or downwardly or, in some cases, with paired explosives, simultaneously, to create a highly elongated generally cylindrical fractured zone interconnecting productive zones of such a thick formation. The spacing and explosive yields are selected therein to provide intersecting open fracture zones as well as to obtain enhancement of the areal extent and number of fractures by shock reflection effects. The Nordyke technique facilitates economical operation using multiple explosives which are of a yield or in which the yields of simultaneously fired explosives which minimize seismic and other hazards.

Accordingly it may be seen that varied procedures for using nuclear explosives and particularly multi-explosive detonation procedures may offer highly beneficial results. Such a procedure should facilitate production of hydrocarbons and natural gas from thick petroliferous formations of the' character described to assist in alleviating the shortage caused by ever increasing depletion of deposits providing economical results by conventional procedures.

SUMMARY OF THE INVENTION The present invention relates generally to the use of sequential nuclear explosive detonations for fracturing and interconnecting subterranean geological formations and, more particularly to an improved procedure in which a series of nuclear explosives are emplaced as a vertically spaced array and are detonated sequentially upward to effectively fracture and interconnect strata therein using a minimum number and yield of explosrves.

Estimated increase in reserves of natural gas in [our major Rocky Mountain basins assuming effective use of nuclear explosives Aerial Increaxed extent with Number Total recovery productive Assumed of known sand Productive using NE potential, productive gas-bearing thickness, thickness, trillion Basin mi. area, rni. formations it. cubic it.

Uinta 8, 900 1,800 4 1,700 680 61 Piceance. 3,900 800 4 1,200 480 19 Green Ri 19,000 4, 000 7 2, 500 1,000 199 San Juan 600 2,000 3 1,100 440 38 Total 317 c.f. C. H. Atkinson Nuclear Fracturing Prospects for Low Permeability Hydrocarbon Reservoirs in the United States, U.S. Department of the interior, Bureau of Mines, Bartlesville Oklahoma. For stimulating such a thick formation to provide effective and economic production of hydrocarbons therefrom it is necessary to obtain adequate intercommunication in the vertical direction as well as to obtain radial fracturing to increase effective permeabilities, effective well diameters and the like so as to obtain adequate flow rates of the hydrocarbon as disclosed in the copending application of Milo D. Nordyke, S.N. 89,889, filed Nov. l6,l970, for "Nuclear Explosive Method for Stimulating Hydrocarbon Production from petroliferous Formations. Also, as disclosed therein,

In accordance with the present invention a series of nuclear explosive devices are first emplaced, as described more fully hereinafter, preferably along a single borehole in a generally vertically spaced array at selected levels along a selected interval of a sub-terranean geological formation. Then a lowermost nuclear explosive, having an appropriate yield with respect to the depth of burial and other conditions, described more fully hereinafter, is detonated to produce a nuclear detonation chamber with a chimney extending upwardly therefrom. Conditions are chosen such that an apical void space of sufficient dimensions, e.g., 20 percent to above about 50 percent of the original cavity volume is formed thereby.

The second device, emplaced next upwardly from the first, is then detonated. The spacing between the first and second device is correlated with the explosive size with regards to relevant conditions so that, on detonation of the second device a cavity and chimney is formed somewhat as with the first. Now, however, the shock wave emanating from the lower portion of the detonation cavity and which is directed generally downward creates a severely stressed annular region surrounding a generally cylindrical columnar region lying between said apical void in the first chimney and the cavity produced by the second detonation. As a consequence of blast and gravitational loading along the columnar region cooperating with the stress effects produced by the shock wave in said annular region, the annular region is disrupted with the columnar region moving downward to enter said first apical void space while a highly fractured shear zone is created in said annular region.

The foregoing procedure is repeated sequentially with the remaining explosive devices. In addition to the effects described above, an extensive fracture system is formed radially outward, not only about the detonation cavity and chimney, as in single nuclear detonations, but also about said columnar region and are intercommunicated therewith. Moreover, the fractured generally annular shear zone regions also provide a gas and fluid permeable pathway interconnecting the respective chimney and cavity regions along the vertical array of shot zones so that a relatively large radius, highly elongated generally cylindrical highly pervious region interconnect the various strata in which the array of nuclear explosives are detonated.

With the present technique a somewhat greater spacing with equivalent explosive yield is permitted so that the number and/or explosive yield required to provide comparable results may be reduced. Cost, may be minimized, seismic effects reduced and other beneficial results obtained.

Accordingly it is an object of the invention to provide novel and improved nuclear blasting procedures for use in subterranean geological formations.

Another object of the invention is to provide an improved sequential nuclear detonation procedure for fracturing and intercommunicating subterranean geological formations.

Still another object of the invention is to provide an improved sequential nuclear detonation procedure in which a series of vertically spaced nuclear devices are detonated sequentially upward in a subterranean geological formation under conditions such that fewer and/or smaller yield devices may be employed to obtain comparable increases in radial permeabilities over thick formation intervals.

Other objects and advantageous features of the invention will be apparent in the following description taken with the accompanying drawing, of which:

FIG. 1, is a vertical sectional view of a chimney and associated fracture pattern produced in an underground nuclear explosive detonation;

FIG. 2, is a vertical sectional view of the chimney, associated fracture patterns and intercommunicating fractured shear zone created by sequential detonation of nuclear explosives at spaced locations in a subterranean formation; I

FIG. 3, is a graphical illustration of a gas reservoir petroliferous formation interval together with wire line log data and nuclear explosive emplacement and detonation data;

FIG. 4, is a graphical representation of the cavitygas, pressure-volume relationship used as the driving pressure for calculation of the effects of a 1 kt explosive yield;

FIG. 5, is a graphical illustration of pressure-volume relationships derived from Hugoniot data and measured compressibility for'rock of the interval shown in 7 FIG. 3.

FIG. 6, is a graphical representation of failure criteria developed from shear strength measurements;

FIG. 7, is a comparative graphical representation for various selected formation media;

FIG. 8, is a graphical representation of cavity radii, limit of compressive failure, fracture initiation and shock front for a detonation as shown in FIG. 1 having a l kt yield as above;

FIG. 9, is a graphical representation of the number of cracks (crack number) at various distances from a I kt shot point as above;

FIG. 10, is a graphical representation of measured and calculated particle velocity with range from a l kt shot point as in FIG. I, conducted in Hoggar granite as above;

FIG. 11, is a graphical comparison of scaled acceleration taken as in FIG. 10;

FIGS. 12 and 13, graphically illustrate positions of the shock front, initiation of fracture and cavity radii for calculations 4 and 5 in the specification involving 40 and kt explosions, respectively;

FIGS. l4, l5 and 16, graphically illustrate radial stress, shear stress and particle velocity as a function of time when the cavity is in quasi-equilibrium, for calculation No. 4 involving a 40 kt explosion;

FIG. 17, shows the crack number for calculations 4 and 5 as a function of distance horizontally;

FIGS. 18 and 19, present scaling curves for the formation interval of FIG. 3;

FIG. 20, is a graphical illustration of peak over pressures vs. scaled range;

FIG. 21, shows peak particle velocity vs. scaled range;

FIG. 22, shows the scaled acceleration vs. scaled range;

FIG. 23, is a graphical representation of the ratio of the height of the interval stimulated to cavity radius, (I-I/R as a function of the number of explosives and spacings;

FIG. 24, is a graphical illustration of the relative effect on particle velocity by interaction of the shock and tensile waves midway between shot point b and lower chimney top of FIG. 2; and

FIG. 25 portrays peak radial overpressures and spall velocity at the top of the lower chimney top in FIG. 2.

DESCRIPTION OF THE INVENTION The teachings of the invention may be utilized in a wide variety of subterranean formations for various purposes. However, the procedures described herein are particularly adaptable for increasing or stimulating production of petroleum hydrocarbons, especially gaseous hydrocarbons, from thick, low-permeability petroliferous formations. The formation modifying effects may also be found applicable, e.g., for in situ retorting of oil shale, mineral recovery, etc., by procedures known in the art.

Several low-permeability petroliferous reservoirs ennumerated hereinbefore and others known to exist contain very large quantities of gas which may be treated by the present procedure. Particular reference will be made herein, for illustrative purposes, to treatment of formations in the Bridger Basin of Wyoming. The rock characteristics, overburden pressures and other factors are quite different from those encountered with past underground nuclear shots. For example, sandstone layers, among those of interest for nuclear stimulation, do not resemble those of other shots, e.g., Gasbuggy. This material has a high proportion of high silica grainto-silica grain contact for which the strength curve resembles that of Hoggar Granite (French North African nuclear testing area in North Africa). This is the hardest rock reported to be encountered for nuclear explosive testing. The high strength tends to reduce the amount of rock fractured but concurrently, the better grain-to-grain contact tends to enhance the localized number of fractures as compared to rocks, such as those encountered, e.g., in Gasbuggy, which contains clay and other materials tending to make the material metaclastic, i.e., weaker and tending to undergo plastic flow. In the socalled tight or low permeability reservoir zones permeabilities may range as low as of the order of about 0.001 md to 0.100 md (millidarcy) and still be suitable for treatment by methods of the present invention. The porosity may generally range below about 15 percent and usually below about percent. The gaseous pressure of hydrocarbons, i.e., the formation pressure may approach hydrostatic or lithostatic levels and therefore be of the order of thousands to 10 of thousands pounds per square inch as measured under static flow conditions. It will be appreciated that the procedure may also be applied in partially depleted oil and gas reservoirs in which the combination of pressure-permeability conditions have declined below the level at which economic recovery remains, to intercommunicate low-productivity zones with the recovery system as well as to those having too low an initial permeability.

Procedures as disclosed in the aforesaid application of Milo D. Nordyke and in the prior art, e.g., of page 974, et. seq. of the aforesaid Proceedings, may be used herein for emplacing the nuclear explosives. More specifically emplacement of the series of explosives is effected preferably, by means of a single borehole, which may be considered to eventuate in a production well. In developing an extensive area, well spacings of 320 or 640 or other acreage as in conventional oil and gas field practice may be utilized. Potentially productive zones may exist at depths ranging from 5,000 to 20,000 feet or deeper, overlain by a relatively impervious caprock or other barren region. Sedimenta ry regions in which productive zones may be situated can comprise various strata, lenses, and beds of silty materials, sandstones, carbonaceous layers such as coals and shales, dolomite, argillaceous, carbonate and other reservoir materials. For present purposes, the thickness of continuous or interbedded intervals which are to be treated will usually be in excess of the 300500 feet, which can be treated using single explosives under permissive seismic limits and be as large as several thousand feet, e.g., 3,0005,000 feet. However, with severe seismic limits, two or more small yield devices may be used in place of a larger device even in the thinner zones.

Although the individual devices may be lowered one at a time, emplaced and detonated at successively higher levels, it is preferred that all of the explosives be emplaced simultaneously as a composite string of nuclear explosives, disposed in a suitable canister together with interposed seal and stemming arrangements, and the like, interconnected by cable or mechanical linkages. A firing cable may be included in the string leading to time delay devices within the nuclear explosive canister set to fire sequentially upward. Individual firing cables might be used; however, some hazard exists that shock waves might sever cables leading to unexploded devices. Arrangements corresponding to those used with conventional explosives may generally be used, e.g., stepping relays or clockwork set into operation by a firing pulse signal dispatched from the surface or by other means disclosed in the aforesaid application of Milo D. Nordyke.

Once the explosives have been emplaced and upper portions of the entry well are stemmed, the lowermost explosive is detonated, either as initiated by the firing pulse directly and simultaneously with setting off the delayed sequence timer mechanisms, or after a time delay, if desired. On detonation of the lowermost device, a shock wave, i.e., a stress discontinuity of thousands of megabars in magnitude propagates outwardly in all directions from the shot point depositing energy therein and being attenuated radially until, at long distances from the source, it propagates elastically. As shown in FIG. 1 of the drawing, at shot point a, there is initially released enough energy to vaporize the rock in amounts of the order of 70 tons per kiloton of explosive energy followed by a small region of melted rock and a fracture region. The cavity formed by the vaporized region of which the lower hemispherical portion 210 remains in FIG. 1, expands rapidly until the pressure in the cavity is in equilibrium with the stresses in the rock. This equilibrium point is defined as the cavity radius, Rc. By processes not well understood at the present time, the equilibrium stresses are disturbed and collapse of the upper hemisphere of the cavity is initiated to fill the cavity with rubble. Once initiated, the collapse generally continues rapidly until it is terminated by either a natural arch 22a or the top is supported by fragment bulked rock or rubble zone 23a of the collapsed region. The collapsed region has been described as a chimney because of its usual cylindrical shape, with the axis of symmetry oriented perpendicular to the bedding. The chimney walls are indicated by reference character 24a. The height above the shot point at which collapse terminated is defined as the chimney height. The radius of the chimney may vary between I to 1.4 R For the purposes of the invention conditions are selected to provide void space 26a in apical portions of the chimney as mentioned hereinbefore A somewhat hard brittle rock without too much metaclastic flow property will generally cave to produce a chimney with a void therein. The original cavity is surrounded by a crushed or pulverized annular spherical zone 27a extending to about 1.6 R and a highly shear fractured zone 28a extending-outwardly therefrom to about 2.5 R In this composite zone the fractures and spaces between the various fragments remain open providing a high permeability path for fluids and gases emerging from the surrounding formation to pass therethrough to enter the chimney. Void space proportions of the order of 20 percent are common, however, the proportions may vary considerably. Outwardly from zone 28, a further zone 29a, extending approximately 5.0 R, from the shot point, is created in which a relatively few radially oriented fractures 31a are formed. These latter fractures are generally closed and are usually too few in number to markedly affect permeability as contrasted to the dense pattern of intersecting fractures created in zone 28.

Subsequently to detonation of the first nuclear explosive at a shot point a, a second nuclear explosive disposed next suprajacent thereto at shot point b as shown in FIG. 2, after an elapsed time in excess of, e.g., about 1 to 5 minutes up to several hours when collapse of the chimney is substantially complete and the void space 26a is formed, is detonated. For Hoggar granite a scaling law has been developed on the time of collapse where t (min) 1.25 W l/3 0.52 where W= kilotons. For 40 kt, t 3.8 minutes. Similar scaling relations can be developed for other rock. Detonation effects above shot point b are similar to those produced by the first explosive above shot point a and as indicated by similar reference characters. However, below shot point b, the crushed zone 27b is displaced downwardly as indicated at 32b and a generally cylindrical or slightly barrelshaped plug portion 33 of the formation is also displaced downwardly somewhat into apical void space 26a while a generally cylindrical fractured shear zone 34 is created about plug 33. The plug 33 is transected by downwardly bowed shear planes 36 but otherwise is not highly fractured. However, lower portions undergo extensive fracturing and spall downwardly through the top 22a of the first nuclear chimney to fill void space 26a with additional rubble 37. Bottom portions of cavity b and crushed zone 27b form a depressed disturbed zone 38. Some additional fracturing (not shown) can be expected radially outward from the shear zone 34 and especially in adjacent portions of fractured zones 29a, 29b.

As a consequence the rubble-filled nuclear chimneys are interconnected by the shear zone 34 to provide for free flow of fluids and/or gas therebetween. Moreover, the open fractured zones 28a, 281; also are in fluid and gas flow communication with the nuclear chimneys and/or shear zone 34 as are any open radial fractures about shear zone 34. As in previous nuclear stimulation practice the effective radius of the well is greatly increased while the effective height is increased even more than in previous multiple explosive practice.

Following detonation of the second explosive at shot I point b the procedure is repeated sequentially until all of the devices have been detonated. Each explosion cooperates with the next previously fired shot to produce a further extension (not shown) of the formation stimulating fracture system to cover the selected interval or intervals in the formation. In effect, the completed interconnected system can be considered overall as a "nuclear chimney albeit, highly elongated insofar as stimulation of the formation, is concerned. Subsequent to expiration of an appropriate period of time, e.g., to allow formation subsidence, distribution of heat, decay of radioactive species, etc., the well bore above the fractured zone is reopened to connect the intercommunicated fracture system to surface production facilities. Otherwise production wells may be drilled to connect with the fracture system or elongated nuclear chimney" as appropriate.

In recapitulation it may be noted that when the first explosive at, a, is detonated, a chimney 24a, crushed zone 27a, shear fracture zone 28a and stressed region proximate chimney roof 22a is formed as shown in FIG. 1. The rock in the stressed region above the chimney is in an unstable stress state and in the process of readjustment due to formation of the chimney. Because of this stressed condition, the effective shear strength of the rock is reduced in this location.

The second explosive at, b, detonated a spaced distance above the first chimney, propagates a shock wave generally along plug portion 33 which refractures the prestressed region and reflects off the existing chimney as a tensile wave. The particle velocity in location'l (FIGS. 2 and 24) is increased markedly under shock loading, then decays due to the high shear stresses. The reflected tensile wave from the chimney increases the velocity again as it passes, spalling the rock. The cavity created by the second explosion is in a quasi-equilibrium state at the time the reflected tensile wave reaches it. The cavity pressure then drives the rock lying generally below the cavity formed by the second detonation down into the lower chimney void, i.e., at 37, shearing along the annular zone 34 which has previously been weakened by the tensile wave. The logical analysis of the shock, spall, and gas acceleration phenomena, set forth below, is based on analysis of cratering experiments (c.f., Terhune, Stubbs and Cherry, Nuclear Cratering on a Digital Computer, page 334, et. seq., of the aforesaid Proceedings). The relative magnitude of each effect depends on yield of the second explosive and on the distance between this explosive and the free surface of the existing chimney.

Overburden pressures are minimal in cratering experiments, resulting in large spall effectsand gas drive pressures of as much as 200 bars. With deeply buried explosions, e.g., with overburden pressures such as exist at 10,000 feet depth, velocity enhancement from spall is severely reduced and is confined to a cylindrical region about the axis connecting the two explosives. However,.cavity pressures will equalize at about 1 kbar (kilobar), providing considerable enhancement of the gas acceleration phase.

Peak surface velocity measurements made on cratering experiments indicate that surface velocities of 34 m/sec or greater are sufficient to form craters, and velocities of 24 m/sec are sufficient to form retarcs. These velocities correspond to scaled distances between the explosive and the free surface of 51 m/W" and 61 m/W" respectively. (Meters/Kiloton On this basis, for a Wagon Wheel, i.e., Bridger Basin, type Sandstone, discussed more fully hereinafter, explosive spacing up to 12.5 R, is effective to produce a continuous chimney. However, it should be noted here I that there is a possibility that the assumptions regarding In this event a somewhat closer spacing between the two explosives is used to present a higher probability of complete collapse in the inter-explosive region. Thus, it is considered advisable that the explosive spacing be maintained between 7.5 R and 10 R for initial operations in Wagon Wheel type sandstone and to increase the spacing in subsequent operations as experience is acquired.

Generally speaking, in accord with the invention, spacings between successive detonations may be in the range of about 7.0 R to about 12.5 R to minimize the number and/or explosive yields required. it may be noted, however, that described effects may also be achieved with closer spacings in the event that such a configuration is desired. in the event that it is desired to detonate any pair or greater plurality of the emplaced explosives simultaneously, the spacing must be reduced, i.e., below about 7.0 R Spacings in the range of about 5.0 to 7.0 R may be used between simultaneously fired devices. Such an operation may be performed after a lower explosive is fired or first, to create a chimney with an apical void space for subsequent detonation of another explosive thereover. While the lower explosives must be emplaced sufficiently deep for containment in order for an appropriate chimney to form, the uppermost need only be emplaced sufficiently deep, i.e., to have a depth of burial (D.O.B.) to assure adequate cavity pressure to afford the requisite gas acceleration. Nuclear explosive sizes may range, e.g., upwardly from a minimum of at least as low as kilotons as determined by economics. It is usually preferable to use as large yields as permitted by BOB. or seismic restrictions since cost of the explosive increases slowly with yield and fracturing effects are more economical. Explosion yields may be as large as 100 kt, 150 kt, 200 kt, or larger if conditions permit. In the event simultaneous detonations are used in combination with sequential, as described, the cavities tend to have a flattened ellipsoidal configuration with a somewhat greater horizontal shear fracture radius. Nuclear explosive devices of the type disclosed by Byron C. Groseclose et al, in a copending application entitled, Underground Engineering Nuclear Explosive, USAEC Case No. S-40,525, are particularly useful for practice of the present invention;

Nuclear explosive size and appropriate spacing can be determined by calculational procedures disclosed in the aforesaid paper entitled, Nuclear Cratering on a Digital Computer, R. W. Terhune et al., page 334 et. seq. of said Proceedings with appropriate modification for adaptation to the different conditions applicable herein as mentioned above. Cratering with nuclear explosives is essentially a wave propagation phenomenon for which calculational procedures, i.e., TENSOR and SOC, have been developed and applied in considering detonation effects in various media as disclosed in various references cited in the foregoing paper and summarized hereinafter.

In all wave propagation problems, the boundary conditions determine the nature of the solution which in usual cratering practice are (l) the cavity formed by the explosion and (2) the ground surface. For purposes herein, the cavity may still comprise one boundary but now the second boundary to be considered is the top surface 22a, 22b, etc., of the chimney formed by a previously detonated explosive. The second boundary provided by such an inverted geometry differs considerably from the free surface (2) above, especially in the stresses present in the rock proximate the top of the cavity, in the direction in which lithostatic pressure changes and particularly in the configuration of the displaced plug region as compared to the generally conical shaped crater formed with a ground surface boundary. In some respects the present configuration may be considered to be an inverted crater with the spalled material corresponding to the ejecta albeit the crater mouth is convergent rather than divergent.

The stress wave interaction on the foregoing boundaries divides the process of crater formation into four observable, sequential phases: shock (compressive wave from cavity to ground surface), spall (rare-faction wave from ground surface to cavity), gas acceleration (recompaction wave toward ground surface) and ballistic trajectory (free fall).

THE CALCULATIONAL MODEL For predicting surface crater geometry without merely scaling from past explosions, a numerical technique has been developed as discussed in the aforesaid paper which integrates the conservation laws of mass momentum and energy on a digital computer. This numerical technique replaces the continuous spatial distribution of stress, density, velocity, etc., with a set defined at discreet positions (zones) in the medium.

At any given time the stress, density, coordinates, and particle velocity of each zone is known. The conservation of momentum equation in differenced form provides a functional relationship between the applied stress field and the resulting acceleration of each point in the grid. Accelerations produce new velocities when allowed to act over a small time increment, At; velocities produce displacements, displacements produce strains, and strains produce a new stress field. Time is incremented by Ar, and the cycle is repeated.

The calculations are simplified when a degree of symmetry is specified. The SOC code integrates the conservation equations written in spherical symmetry (there is only a radial direction of motion permitted), while the TENSOR code allows study of cylindrically symmetric problems (such as craters) where two spatial variables must be considered.

The' manner in which the strain is related to stress is called the equation-of-state of the material. This equation-of-state must describe the various modes of material behavior (gas, fluid, solid) and allow for acceptable transitions among the modes. It must be determinable before the shot. Preshot logging and core tests have been used to satisfy this last requirement. Preshot logging measurements are extremely important in determining the average properties of the entire rock structure and the layers of impedance mismatch. These logs also are needed for proper selection of the core samples and verification that the tests are representative of the site.

More particularly, once the hole is drilled, in situ velocity and density logs are run. From the density, compression, and shear velocity logs, core samples are selected for high pressure testing, mineralogy, porosity, and water content measurements. High pressure testing consists of (l) hydrostatic compressibility measurements, both loading and unloading, up to 40 kbar, (2) Hugoniot (150-700 kbar) data, and I-lugojiot elastic limit if measurable, and (3) shear strength for confining pressures up to kbar.

A best fit for Poissons ratio is determined from the in situ logging data and the initial bulk modulus as determined from the hydrostatic compressibility measurements.

With the completion of the equation-of-state, a SOC calculation is made to determine the radius of vaporization, develop the gas tables for the vaporized rock, and check the EOS for errors. A TENSOR grid is established whereby the energy of the device is distributed uniformly throughout the cavity. The problem is monitored until the shock, spall and gas acceleration phases are completed and/or large pressure or velocity gradients are no longer present.

MATERIAL CHARACTERISTICS IMPORTANT IN CRATERING The equation-of-state (EOS) defines the cratering efficiency of a medium; that is, the equation-of-state specifies the amount of internal energy of the explosive which will be converted into kinetic energy in the plug region 33 below the explosive by shock, spall, and gas acceleration.

The following four equation-of-state parameters are important in determining cratering efficiency:

compressibility Porosity (compactability or compressibility) Water content Strength.

The first three relate to the hydrostatic loading and unloading characteristics of the medium. The fourth limits the permissible deviatoric stress in the rock.

Further details of procedures relevant to the foregoing will be summarized for illustrative purposes in the following example relating to an operation termed Wagon Wheel" designed for use in the Bridger Basin near Pinedale, Wyoming.

EXAMPLE Considerations herein are directed to intervals of from 9,000 ft. to 10,500 ft. and from 11,300 to 11,800 feet of a well section shown in FIG. 3, wherein general stratigraphy cored sections and selected wire line logs are shown. Pressure volume relationships to 40 kbars are indicated in FIG. 5, for which the corresponding failure envelope was determined. It will be appreciated that the relevant parameters for other rock formations can be derived in a fashion similar to that disclosed herein. Shock I-Iugoniot measurement is given in Table 1.

In the static tests it was also noted that in a pressure excursion up to 40 kb and back to zero there was about 1 percent irreversible compaction.

Wet 2.440 5.50 2.00 269 0.261 Dry 2.430 5.46 2.01 267 0.260 Dry 2.430 5.53 2.00 269 0.263 Wet 2.438 5.20 1.34 0.304 Wet 2.451 5.16 L34 170 0.302 Dry 2.422 5.16 1.35 169 0.305 Dry 2.398 5.l7 1.34 167 0.309

p Bulk density in gm/cm U, shock velocity mlmsec U, partical velocity m/msec o principal stress kbars V specific volume cmlgm The driving pressure for the calculations was the cavity pressure-volume curve shown in FIG. 4. This curve is based on the S O, 1% H O gas equation of state and adiabatic expansion relationship developed at Lawrence Radiation Laboratory (LRL). (c.f. Butkovich, l. R., The Gas Equation of State for Natural Materials, UCRL-l4729, Jan. 24, 1967).

The calculation is started at the time when the vaporized cavity is formed so thatthe computer does not need to consider whether hydrodynamic heating vaporizes any more rock. The vaporization radius is calculated from the expression R,, CW" (R, in meters, W in kilotons) where C 1.9 for sandstone of density 2.45 gm/cm. For other rock types any other appropriate value for C is chosen from published values or determined. The initial pressure of the cavity gas at the end of the vaporization phase is 1.55 megabars.

FIG. 5 shows the pressure-volume relationship of the rock used as an average between the depths of 9,000 feet and 12,000 feet. This is based upon both the Hugoniot data and the measured compressibility. An average Poissons ratio of 0.2 was selected based on the one-dimensional strain tests.

FIG. 6 shows the failure criteria used as developed from tl shear strength measurements in the form of K, versus P as defined below for the particular operation, e.g., Wagon Wheel withv those of other experiments. On the basis of porosity and water content, all experiments in tuff and alluvium and their associated scaling laws can be eliminated from consideration. Eliminating others for a variety of reasons leaves experiments in NTS granite, Gasbuggy and the Hoggar granite, Derlich, 8., Underground Nuclear Explosions Effects in Granite Rock Fracturing," of said Proceedings. Table 2 compares the material EOS parameters with Wagon Wheel.

TABLE 2 MEDIUM p H,O Kmax NTS "l-lugoniot elastic limit for NTS granite is 7.5 kbars.

pn initial density gm/cc V, compressional velocity m/millisec o Poisson's ratio 11,0 water content by weight d) porosity in Kmax maximum shear strength (kbars) 8% porosity above 60% saturation :1- Gasbuggy average of 0.14 loading and 0.3 unloading In FIG. 7, the strength curves for the foregoing media are compared with Wagon Wheel sandstone which indicates that the strength data of the Wagon Wheel medium is similar to that of the l-loggar Granite.

The French experiments in the Hoggar granite were at low to moderate yields at depths between 200 to 400 m. The scaling laws developed for the media are given below.

1. Cavity radius, defined as the interface between the melt and the solid rock. R 7 .3 W" and also 52W pgh+0.

where 'y 1.03 pgh overburden pressure C, strength term in bars 120 C, 320 R Cavity radius in meters W= Explosive yield in kilotons I 2. Radius of crushed zone between the cavity and this radius the rock has been pulverized. R, X W (meters, kilotons also 1.3 R R,, 1.8 R

3. Radius of fracture this radius is also the limit to which theFrench assumed the chimney will grow and, if consistent with SOC calculations, is the maximum extent of tangential fracture.

R,= 26 W" (meters, kilotons) 4. Radius of stress zone this zone is defined by the drill core fracturing in parallel disks, indicating a highly stressed region is being relieved. Also, some preshot or shock induced fractures are encountered.

R 35 W" (meters, kilotons in order to compare the Wagon Wheel rock with the Hoggar granite, a SOC calculation, using the Wagon Wheel EOS, was made for a yield of 1 kt with an overburden pressure of 70 bars representing the initial conditions of the Hoggar data.

FIG. 8 shows the cavity radius, limit of compressive failure, fracture initiation and the shock front as a function of time. Table 3 compares the calculational results with the Hoggar granite experience for this 1 kt explosive yield.

in bars TABLE 3 Radius Hoggar (m) Calculation Granite The radius of the crushed zone was determined by comparing the increase in the crack number for each zone between 25 msec and 50 msec as shown in Table 4. The radial distance is given at the time of 50 msec. The assumption is that the crushed zone was formed by continued refracture over a period of time. This is further emphasized in FIG. 9 which shows the number of cracks (fractures) as a function of distance.

FIG. 10 compares the measured peak particle velocity at the shock front for Hoggar granite with the SOC calculation using the Wagon Wheel EOS. FIG. 11 is a comparison of the scaled acceleration. The solid curve in FIG. 11 is a least square fit to the data and also the maximum acceleration at the shock front as calculated by SOC. The dashed curve is the SOC peak velocity divided by the rise time to give a mean particle acceleration. Thus, on the basis of all available data it seems that the experiments in l-loggar granite provides an excellent model for Wagon Wheel.

TABLE 4 CRACK NUMBER ZONE NUMBER T=25 msec 970 1 3 12.016 971 2 5 1 1.744 972 2 4 1 1.474 973 2 4 1 1.210 974 2 4 10.949 975 2 4 10.694 976 3 6 10.444 977 3 6 10.200 978 3 6 9.961 979 3 7 9.729 980 4 8 9.504 981 4 8 9.287 982 4 9 9.077 983 5 10 8.876 984 6 l 1 8.683 985 8 15 8.500 986 12 19 8.328 987 16 23 8.165 988 18 26 8.013 989 25 33 7.873 990 332 40 7.743 991 49 58 7.520 992 56 64 7.343 993 58 67 7.210 994 Melt Melt 7.060 995 Gas Gas 6.123

NUMERICAL CALCULATIONS FOR WAGON WHEEL AT DEPTH and 19. Using an adiabatic expansion formulation for the cavity gas as did the French, the equation for the cavity radius is apt R ig/ 7 are for depths of 9,600 feet. Calculations 2, 3, and 6 are at the overburden pressures of Gasbuggy, Rulison, and French (I-Ioggar) experiments respectively.

TABLE W Povb Rv Rc Pc Rsf R(mxf) CALC (kt) (kb) (m) (rn) (kb) (in) where W is the yield in kilotons Povb is the overburden pressure Rv is the radius of vaporization Re is the final cavity radius Pc is the final cavity pressure Rsf is the shear fracture radius Rmxf is the maximum possible radius of fracture FIGS. 12 and 13 show the positions of the shock front, initiation of fracture, and cavity radius with respect to time for calculations 4 and 5, respectively. The separation between shear failure on shock loading and extension failure on unloading is clearly defined as the separation of the fracture initiation curve from the shock front.

FIGS. l4, l5 and 16 show the radial stress, shear stress, and particle velocity, respectively, as a function of distance at the time the cavity is in quasi equilibrium for calculation No. 4, i.e., at t 120 milliseconds. Between the cavity and the limit of shear fracture radius, the radial stress increases with distance and is the minimum principle stress, i.e., K =(q o, /2 is negative) and thus this is a region where tangential fractures predominate.

Between the limit of shear fracture and the maximum fracture radius, K is positive, indicating that the fractures should be radial in this region. Outside the maximum fracture radius, the rock has been stressed but remains essentially unfractured.

FIG. 17 shows the crack number for calculation 4 and 5 as a function of distance horizontally from the shot point. The crack number is the number of times the failure envelope has been exceeded. Corresponding limits of fracture radii are shown, indicating the relative degree of fracture in these zones.

SCALING LAWS FOR WAGON WHEEL Based on the preceding calculations, scaling curves for Wagon Wheel were developed as shown in FIGS. 18

1.05 to account for the melt 1.550 kb vaporization pressure 2.3 P 1 kb Figure A2 1.14 P l kb 1.9W radius of vaporization cavity pressure at equilibrium in kbars Note: The a used by French is based on shot room void not being vaporized.

where the distance is expressed in meters and the yield (W) in kilo tons.

The cavity pressure is approximately 0.4 kbar greater than the overburden (Table 5), and for pressures less than 1.4 kbars, the use of a 'y 1.14 results in error of less than 5 percent. Substituting, we have The difference between this equation and that developed by the French for Hoggar granite is basically in the y assumed for the cavity gas and a slightly smaller strength term. FIG. 18 shows the above equation plotted for 4 yields as a function of overburden pressure.

FIG. 19 shows the ratio of the various fracture radii, as determined by the SOC calculation, to the cavity radius. The radius of the crushed zone is independent of the overburden pressure, and thus the ratio increases as the cavity radius decreases with depth. The shear fracture radius and radial fracture radius are strongly dependent on the overburden, requiring higher shock stresses to fracture. FIG. 20 shows the peak overpressure at the shock front as a function of scaled distance.

FIG. 21 shows the peak particle velocity as a function 1 (FIG. 24) increases rapidly under'shock loading, then decays due to the high shear stresses. The reflected tensile wave from the chimney increases the velocity again as it passes, spalling the rock. The cavity created by the second explosion is in a quasi-equilibrium state at the time the reflected tensile wave reaches it. The cavity pressure then drives the rock below the cavity formed by the second detonation down into the lower chimney void, shearing along the cylindrical zone which has previously been weakened by the tensile wave as discussed above. FIG. 25 shows the peak spall velocity and radial overpressure at the upper surface of the chimney resulting from the first detonation as a function of the initial spacing of the explosives, assuming a chimney height of2.5 R

CHIMNEY CONFIGURATION Chimneys observed in Hoggar granite are of two types. One is asymmetric perpendicular to the bedding with R R The other is oval with R 1.4 R about 2 R above the explosion point. Both types do not extend beyond the shear fracture radius. United States experience is similar.

The rock from the site of Gasbuggy has a higher ductile matrix content than that from Wagon Wheel; therefore, it is likely that a chimney will form at Wagon Wheel. The chimney is expected to flare outward with a slope of about 5. This is intermediate between the two cases in Hoggar granite and somewhat greater than U.S. experience. It is based on expected particle size and experience in rock flow in ore passes.

FIG. 1 shows the expected chimney and associated fracture pattern for a single explosive at 10,000 feet depth. The crushed or pulverized region extends to 1.6 R the shear fracture to 2.5 R and the maximum radial fracture to 5.1 R The chimney radius measures 1.2 R, at an elevation of 2.0 R above the shotpoint. The total chimney height is 2.5 R Using a porosity of 0.21 for the rubble gives an apical void of 0.5 (50 percent) cavity volumes, and a void height of 0.4 R The maximum chimney height based on a porosity of 0.21 would be 4 R if the chimney were allowed to grow beyond the fracture radius.

Based on permeability measurements in the I-loggar experiments and gas flow test analysis of Gasbuggy, permeability is expected to be greatly enhanced within the shear fracture region. In the radial fracture region, permeability is expected to be slightly higher than the initial value, but beyond this no increase is expected as dilatancy arguments are not applicable. Static equilibrium of the rock around the chimney requires that the radial stress adjust from a maximum to a minimum principle stress. This may result in tangential fractures leading to an increase in permeability. This effect would be greatest above the chimney and negligible below.

In FIG. 3, emplacement D.O.B. for 100 KT of nuclear explosive yield with 7.5 R and R spacings are shown. For comparison, a 6.0 R spacing with 150 kt explosive yield is shown. Comparative percentages of gas expected to be recovered are also shown below.

The data are tabulated below:

Total Res. Slim. 221.4 BCF 221.4 BCF 221.4 BCF Recovered 10.6 10.2 12.3

FIG. 23 graphically relates the number of explosives to the ratio of the spacing to cavity radius (S/R to the ratio of height stimulated to cavity radius (H/R Since R can be determined as indicated above the spacing and number of explosives required for selected intervals may be determined approximately therefrom.

While there have been described in the foregoing what may be considered to be preferred embodiments of the invention modifications in the skill of the art may be made therein without departing from the teachings of the invention and it is intended to cover all such as fall within the scope of the appended claims.

What 1 claim is: 1. A process for producing a highly elongated generally cylindrical chimney region of fractured and fragmented material along a selected interval of a subterranean rock formation comprising:

creating an access bore traversing said selected formation interval in the subterranean formation;

emplacing a first nuclear explosive device at a relatively low position in said access bore within said selected formation interval;

detonating said first nuclear device to produce a first cavity and chimney region extending upwardly therefrom, said chimney having an apical void space therein above a rubble zone wherefor the top of the chimney is in a substantially free standing prestressed condition, said cavity being surrounded by successive crushed, open shear fractured and radially fractured generally spherical concentric zones in said formation;

emplacing a second nuclear explosive device at a second position above the emplacement position of said first nuclear explosive and detonating the second explosive device wherein the spacing between said first and second explosive devices is in the range of from 7.0 R to about 12.5 R wherein R is the radius of the cavity formed by detonation of the respective devices, so that, through interaction of shock wave and gas pressure acceleration phenomena, downwardly from the cavity produced by detonation of the second device, a generally cylindrical transversely fractured plug region of the formation disposed generally between the second cavity and the first chimney is displaced downwardly while lower end portions thereof spall into said apical void space of the first chimney and that a generally cylindrical annular shear fracture zone is substantially simultaneously created about said plug region, said open shear fracture region intercommunicating with the shear fracture, detonation cavity, and chimney created by the respective first and second detonated devices.

2. A process as defined in claim 1 wherein a plurality greater than two of said nuclear explosive devices are emplaced and are detonated sequentially upward from a first lowermost device wherein the spacing between each of said nuclear explosive devices is in the range of from 7.0 R to about 12.5 R and wherein is created a series of nuclear explosion cavity chimney regions with associated shear fracture regions intercommunicated by an annular shear fracture zone disposed about a generally cylindrical fractured plug region disposed between proximal cavity and chimney portionsl 

1. A process for producing a highly elongated generally cylindrical chimney region of fractured and fragmented material along a selected interval of a subterranean rock formation comprising: creating an access bore traversing said selected formation interval in the subterranean formation; emplacing a first nuclear explosive device at a relatively low position in said access bore within said selected formation interval; detonating said first nuclear device to produce a first cavity and chimney region extending upwardly therefrom, said chimney having an apical void space therein above a rubble zone wherefor the top of the chimney is in a substantially free standing prestressed condition, said cavity being surrounded by successive crushed, open shear fractured and radially fractured generally spherical concentric zones in said formation; emplacing a second nuclear explosive device at a second position above the emplacement position of said first nuclear explosive and detonating the second explosive device wherein the spacing between said first and second explosive devices is in the range of from 7.0 Rc to about 12.5 Rc, wherein Rc is the radius of the cavity formed by detonation of the respective devices, so that, through interaction of shock wave and gas pressure acceleration phenomena, downwardly from the cavity produced by detonation of the second device, a generally cylindrical transversely fractured plug region of the formation disposed generally between the second cavity and the first chimney is displaced downwardly while lower end portions Thereof spall into said apical void space of the first chimney and that a generally cylindrical annular shear fracture zone is substantially simultaneously created about said plug region, said open shear fracture region intercommunicating with the shear fracture, detonation cavity, and chimney created by the respective first and second detonated devices.
 2. A process as defined in claim 1 wherein a plurality greater than two of said nuclear explosive devices are emplaced and are detonated sequentially upward from a first lowermost device wherein the spacing between each of said nuclear explosive devices is in the range of from 7.0 Rc to about 12.5 Rc, and wherein is created a series of nuclear explosion cavity chimney regions with associated shear fracture regions intercommunicated by an annular shear fracture zone disposed about a generally cylindrical fractured plug region disposed between proximal cavity and chimney portions produced by the successive detonations.
 3. A process as defined in claim 2 wherein said formation interval is a petroliferous formation interval and wherein the elongated generally cylindrical chimney region of intercommunicated nuclear detonation cavities and chimney provide a high permeability path for egress of fluid and gaseous hydrocarbons from said petroliferous formation. 